Question: Simplify the following expression: $ k = \dfrac{10z - 6}{-3z - 8} + \dfrac{8}{9} $
In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{9}{9}$ $ \dfrac{10z - 6}{-3z - 8} \times \dfrac{9}{9} = \dfrac{90z - 54}{-27z - 72} $ Multiply the second expression by $\dfrac{-3z - 8}{-3z - 8}$ $ \dfrac{8}{9} \times \dfrac{-3z - 8}{-3z - 8} = \dfrac{-24z - 64}{-27z - 72} $ Therefore $ k = \dfrac{90z - 54}{-27z - 72} + \dfrac{-24z - 64}{-27z - 72} $ Now the expressions have the same denominator we can simply add the numerators: $k = \dfrac{90z - 54 - 24z - 64}{-27z - 72} $ $k = \dfrac{66z - 118}{-27z - 72}$ Simplify the expression by dividing the numerator and denominator by -1: $k = \dfrac{-66z + 118}{27z + 72}$